Flow Analysis in Francis Water Turbines

1967 ◽  
Vol 89 (3) ◽  
pp. 445-451
Author(s):  
W. Jansen
Keyword(s):  
Flow Field ◽  
Flow Analysis ◽  
Analytical Techniques ◽  
Small Drop ◽  
Streamline Curvature ◽  
Underlying Theory ◽  
Upper Limits ◽  
Water Turbines ◽  
Flow Reversals ◽  
Streamline Curvature Method

It is the intent of this study to investigate the flow field in Francis water turbines operated at various guidevane settings with the use of analytical techniques. The flow fluid is analyzed with a streamline-curvature method and the underlying theory is discussed briefly. With the analysis, certain lower and upper limits for the guidevane settings can be defined. Within these limits only a small drop-off in efficiency at the extreme settings can be expected. Outside these limits severe cavitation and flow reversals are shown to take place. In the Appendix, it is shown how the analysis can be used to evaluate the effects of different passage and blade geometry on the flow field.

Improved Approach to the Streamline Curvature Method in Turbomachinery

1987 ◽  
Vol 109 (3) ◽  
pp. 213-217 ◽  
Author(s):  
S. Abdallah ◽  
R. E. Henderson
Keyword(s):  
Flow Field ◽  
Velocity Gradient ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Second Order ◽  
Curvilinear Coordinates ◽  
First Order ◽  
Streamline Curvature ◽  
Stators And Rotors ◽  
Streamline Curvature Method

Quasi three dimensional blade-to-blade solutions for stators and rotors of turbomachines are obtained using the Streamline Curvature Method (SLCM). The first-order velocity gradient equation of the SLCM, traditionally solved for the velocity field, is reformulated as a second-order elliptic differential equation and employed in tracing the streamtubes throughout the flow field. The equation of continuity is then used to calculate the velocity. The present method has the following advantages. First, it preserves the ellipticity of the flow field in the solution of the second-order velocity gradient equation. Second, it eliminates the need for curve fitting and strong smoothing under-relaxation in the classical SLCM. Third, the prediction of the stagnation streamlines is a straightforward matter which does not complicate the present procedure. Finally, body-fitted curvilinear coordinates (streamlines and orthogonals or quasi-orthogonals) are naturally generated in the method. Numerical solutions are obtained for inviscid incompressible flow in rotating and non-rotating passages and the results are compared with experimental data.

scholarly journals A procedure for the calculation of flow through axisymmetric ducts

1983 ◽  
Vol 2 (2) ◽  
pp. 92-103
Author(s):  
P. S. Heyns
Keyword(s):  
Flow Field ◽  
Flow Direction ◽  
Governing Equations ◽  
Streamline Curvature ◽  
Flow Through ◽  
Streamline Curvature Method

A procedure for the calculation of flow through axisymmetric ducts as are typically found in turbomachines, is presented. The procedure is based on a streamline curvature method with the governing equations formulated along quasi-orthogonals in the flow field. This formulation allows the procedure to be used for segments of a duct wherein the flow direction is predominantly radial. It is assumed that the flow on specific stream surfaces is isentropic, but normal entropy gradients may exist because of processes which took place upstream of the duct.

A Streamline Curvature Method for Calculating S1 Stream Surface Flow

1984 ◽  
Vol 106 (2) ◽  
pp. 306-312
Author(s):  
S. K. Mao ◽  
D. T. Li
Keyword(s):  
Surface Flow ◽  
Approximation Technique ◽  
Flow Section ◽  
Boolean Expression ◽  
Simple Method ◽  
Stream Surface ◽  
Streamline Curvature ◽  
Calculation Results ◽  
Good Agreement ◽  
Streamline Curvature Method

A streamline curvature method for calculating S1 surface flow in turbines is presented. The authors propose a simple method in which a domain of calculation can be changed into an orderly rectangle without making coordinate transformations. Calculation results obtained on subsonic and transonic turbine cascades have been compared with those of experiment and another theory. Good agreement has been found. When calculating blade-to-blade flow velocity at subsonic speed, a function approximation technique can be used in lieu of iteration method in order to reduce calculation time. If the calculated flow section is of a mixed (subsonic-supersonic) flow type, a Boolean expression obtained from the truth table of flow states is proposed to judge the integrated character of the mixed flow section. Similarly, another Boolean expression is used to determine whether there exists a “choking” of the relevant section. Periodical conditions are satisfied by iterating the first-order derivative of stagnation streamline, which is formed simultaneously. It can be proved that the stagnation streamline formed in this way is unique.

Modeling of Discrete Tip Injection in a Two-Dimensional Streamline Curvature Method

2012 ◽  
Author(s):  
Roland Matzgeller ◽  
Richard Pichler
Keyword(s):  
Rotating Stall ◽  
Streamline Curvature ◽  
Measurement Results ◽  
Compressor Design ◽  
Multistage Compressor ◽  
Physical Effects ◽  
Tip Injection ◽  
Stability Enhancement ◽  
Good Agreement ◽  
Streamline Curvature Method

Fluid injection at the tip of highly loaded compressor rotors is known to be effective in suppressing the onset of rotating stall and eventually compressor instability. However, using such stability enhancement methods in a multistage compressor might not only stabilize certain stages but has also an impact on radial and axial matching. In order to account for tip injection during the early stages of compressor design, this paper focuses on the development of a method to model the physical effects underlying tip injection within a streamline curvature method. With the help of system identification it could be shown that a rotor subject to the discrete jets of tip injection adapts to the varying flow conditions according to a first order model. This information was used to generate a time-dependent input for the steady equations used with a streamline curvature method and eventually to model the unsteady response of the rotor to tip injection. Comparing the results obtained with the enhanced streamline curvature model to measurement results, good agreement could be shown which raised confidence that the influence of tip injection on axial and radial matching was sufficiently captured.

scholarly journals Feasibility Study on Oil Droplet Flow Investigations Inside Aero Engine Bearing Chambers: PDPA Techniques in Combination With Numerical Approaches

1995 ◽  
Author(s):  
A. Glahn ◽  
M. Kurreck ◽  
M. Willmann ◽  
S. Wittig
Keyword(s):  
Numerical Methods ◽  
Flow Field ◽  
Flow Analysis ◽  
Field Analysis ◽  
Oil Droplet ◽  
Droplet Flow ◽  
Aero Engine ◽  
Secondary Air ◽  
Numerical Approaches ◽  
Engine Bearing

The present paper deals with oil droplet now phenomena in aero engine bearing chambers. An experimental investigation of droplet sizes and velocities utilizing a Phase Doppler Particle Analyzer (PDPA) has been performed for the first time in bearing chamber atmospheres under real engine conditions. Influences of high rotational speeds are discussed for individual droplet size classes. Although this is an important contribution to a better understanding of the droplet flow impact on secondary air/oil system performance, an analysis of the droplet flow behaviour requires an incorporation of numerical methods because detailed measurements as performed here suffer from both strong spatial limitations with respect to the optical accessibility in real engine applications and constraints due to the extremely time consuming nature of an experimental flow field analysis. Therefore, further analysis is based on numerical methods. Droplets characterized within the experiments are exposed to the flow field of the gaseous phase predicted by use of our well-known CFD code EPOS. The droplet trajectories and velocities are calculated within a Lagrangian frame of reference by forward numerical integration of the particle momentum equation. This paper has been initiated rather to show a successful method of bearing chamber droplet flow analysis by a combination of droplet sizing techniques and numerical approaches than to present field values as a function of all operating parameters. However, a first insight into the complex droplet flow phenomena is given and specific problems in bearing chamber heat transfer are related to the droplet flow.

Unsteady Flow Analysis and Vibratory Stress Predictions for a High Work Single Stage Turbine Blade

2012 ◽  
Author(s):  
Kurt Weber ◽  
Girish Modgil ◽  
Steve Gegg ◽  
Shyam Neerarambam ◽  
Moujin Zhang
Keyword(s):  
Flow Field ◽  
Strain Gauge ◽  
Flow Analysis ◽  
Forced Response ◽  
Single Stage ◽  
Turbine Stage ◽  
Rotating Blade ◽  
Gauge Data ◽  
Unsteady Flow Analysis ◽  
High Work

The flow field in High-Work Single-Stage (HWSS) turbines differs from traditional turbine flow fields. Operating at increased pressure ratios, wakes and trailing edge shocks at the exit of the vane are more likely to cause a vibratory response in the rotating blade. This flow field can produce increased excitation at harmonics that correspond to the vane passing frequency and harmonics higher than the vane passing frequency. In this paper, blade vibratory stresses in a HWSS gas turbine stage are predicted using unsteady pressures from two Rolls-Royce in-house flow codes that employ different phase lagged unsteady approaches. Hydra uses a harmonic storage approach, and the Vane/Blade Interaction (VBI) code uses a direct storage approach. Harmonic storage reduces memory requirements considerably. The predicted stress for four modes at two engine speeds are presented and are compared with rig test strain gauge data to assess and validate the predictive capability of the codes for forced response. Strain gauge data showed the need to consider harmonics higher than the fundamental vane passing frequency for the max power shaft speed and operating at the conditions. Because of this, it was a good case for validation and for comparing the two codes. Overall, it was found that, stress predictions using the Hydra flow code compare better with data. To the best of the authors’ knowledge, this paper is a first in comparing two different phase lagged unsteady approaches, in the context of forced response, to engine rig data for a High-Work Single Stage turbine.

scholarly journals Experimental and CFD Studies of the Hydrodynamics in Wet Agglomeration Process

2018 ◽  
Vol 2 (3) ◽  
pp. 32 ◽  
Author(s):  
Benjamin Oyegbile ◽  
Guven Akdogan ◽  
Mohsen Karimi
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
Flow Analysis ◽  
Outer Region ◽  
Tangential Velocity ◽  
Numerical Code ◽  
Cfd Model ◽  
Rotating Disc ◽  
Batch Mode ◽  
Agglomeration Process

In this study, an experimentally validated computational model was developed to investigate the hydrodynamics in a rotor-stator vortex agglomeration reactor RVR having a rotating disc at the centre with two shrouded outer plates. A numerical simulation was performed using a simplified form of the reactor geometry to compute the 3-D flow field in batch mode operations. Thereafter, the model was validated using data from a 2-D Particle Image Velocimetry (PIV) flow analysis performed during the design of the reactor. Using different operating speeds, namely 70, 90, 110, and 130 rpm, the flow fields were computed numerically, followed by a comprehensive data analysis. The simulation results showed separated boundary layers on the rotating disc and the stator. The flow field within the reactor was characterized by a rotational plane circular forced vortex flow, in which the streamlines are concentric circles with a rotational vortex. Overall, the results of the numerical simulation demonstrated a fairly good agreement between the Computational Fluid Dynamics (CFD) model and the experimental data, as well as the available theoretical predictions. The swirl ratio β was found to be approximately 0.4044, 0.4038, 0.4044, and 0.4043 for the operating speeds of N = 70, 90, 110, and 130 rpm, respectively. In terms of the spatial distribution, the turbulence intensity and kinetic energy were concentrated on the outer region of the reactor, while the circumferential velocity showed a decreasing intensity towards the shroud. However, a comparison of the CFD and experimental predictions of the tangential velocity and the vorticity amplitude profiles showed that these parameters were under-predicted by the experimental analysis, which could be attributed to some of the experimental limitations rather than the robustness of the CFD model or numerical code.

scholarly journals Non-premixed swirl-type tubular flames burning liquid fuels

2018 ◽  
Vol 846 ◽  
pp. 210-239
Author(s):  
Vinicius M. Sauer ◽  
Fernando F. Fachini ◽  
Derek Dunn-Rankin
Keyword(s):  
Flow Field ◽  
Swirling Flow ◽  
Flame Structure ◽  
Flow Analysis ◽  
Liquid Fuels ◽  
Reacting Flow ◽  
Surface Mass ◽  
Surface Mass Transfer ◽  
Incompressible Viscous Flow ◽  
Porous Walls

Tubular flames represent a canonical combustion configuration that can simplify reacting flow analysis and also be employed in practical power generation systems. In this paper, a theoretical model for non-premixed tubular flames, with delivery of liquid fuel through porous walls into a swirling flow field, is presented. Perturbation theory is used to analyse this new tubular flame configuration, which is the non-premixed equivalent to a premixed swirl-type tubular burner – following the original classification of premixed tubular systems into swirl and counterflow types. The incompressible viscous flow field is modelled with an axisymmetric similarity solution. Axial decay of the initial swirl velocity and surface mass transfer from the porous walls are considered through the superposition of laminar swirling flow on a Berman flow with uniform mass injection in a straight pipe. The flame structure is obtained assuming infinitely fast conversion of reactants into products and unity Lewis numbers, allowing the application of the Shvab–Zel’dovich coupling function approach.

Numerical Simulation of Sand Erosion Phenomena in Square-Section 90 Degree Bend With Linear/Nonlinear RANS Turbulence Models

2007 ◽  
Author(s):  
Masaya Suzuki ◽  
Kazuaki Inaba ◽  
Makoto Yamamoto
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Turbulence Models ◽  
Solid Particles ◽  
Two Phase ◽  
Streamline Curvature ◽  
Sand Erosion ◽  
Rans Turbulence Models ◽  
Wall Deformation ◽  
Bend Flow

Sand erosion is a phenomenon where solid particles impinging to a wall cause serious mechanical damages to the wall surface. This phenomenon is a typical gas-particle two-phase turbulent flow and a multi-physics problem where the flow field, particle trajectory and wall deformation interact with among others. On the other hand, the sand erosion is a serious problem to install pneumatic conveying systems for handling abrasive materials. Incidentally, the bend erosion is typical target of sand erosion experiments and is useful for verification of numerical simulations. Although, the secondary flow which occurs in such a flow field including streamline curvature cannot be reproduced by the standard k-ε model. To predict this flow field, a more universal model which can estimate anisotropic Reynolds stress is required. In the present study, we simulate sand erosion of 90 degree bend with a square cross-section. We use some linear/nonlinear turbulence models to predict the secondary flow of the bend. Besides, the performance of each model to predict clear/eroded bend flow field is studied.

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